01-NSW · Maths Extension 1

Higher School Certificate · NESA· 2026

HSC Mathematics Extension 1: complete 2026 guide (modules, exam, scaling, strategy)

A complete 2026 guide to HSC Mathematics Extension 1. Module breakdown across Year 11 and Year 12 content, exam structure, scaling (Ext 1 is one of the highest-scaling HSC subjects most years), study strategy, and links to every dot point and deep guide we have.

Browse guides Syllabus dot points (60)Exam trends ATAR calculator

HSC Mathematics Extension 1 is the 1-unit course that sits on top of Mathematics Advanced. Together they form a 3-unit study and the two papers are sat as separate HSC exams. Extension 1 is taken by students aiming at high ATARs, STEM degrees, or commerce and actuarial pathways.

This page is the index. Below you will find the topic breakdown, exam structure, scaling notes, study strategy, and links to every dot point and deep guide we have.

Two syllabuses are live in 2026

HSC Mathematics Extension 1 is in a syllabus transition.

If you are sitting the HSC in 2026 (currently Year 12), you follow the 2017 syllabus. Topics: Functions, Trigonometric Functions, Calculus, Combinatorics (Year 11 ME-A1), Proof by Induction, Vectors (Year 12 ME-V1), and the Binomial Distribution.

If you are starting Year 11 in 2026 (HSC 2027 onwards), you follow the new 2024 syllabus. Most content is identical, with adjusted emphasis and updated assessment structures. Vectors and projectile motion are unchanged in scope. Statistical inference is slightly expanded.

This hub covers both syllabuses where they differ. Check with your school which syllabus your cohort is on.

The seven topics

Functions (ME-F1, ME-F2)

Polynomial functions, division algorithm, remainder and factor theorems, multiple roots and multiplicity, polynomial inequalities, parametric equations, and graphs of reciprocal and rational functions.

Trigonometric functions (ME-T1, ME-T2, ME-T3)

Inverse trigonometric functions ( $\arcsin$ , $\arccos$ , $\arctan$ ) including their graphs, domains and ranges. Sum, difference, double and product-to-sum identities. The auxiliary angle technique. General solutions of trigonometric equations and the t-formula (Weierstrass substitution).

Calculus (ME-C1, ME-C2, ME-C3)

Related rates and exponential growth and decay. Integration by substitution, including reverse chain rule cases. Integration giving inverse trigonometric functions. Volumes of revolution. Separable differential equations and their applications. Projectile motion.

Combinatorics and the binomial theorem (ME-A1)

Permutations, combinations, the pigeonhole principle, and the binomial theorem with Pascal's triangle.

Proof by mathematical induction (ME-P1)

Induction on series, divisibility statements, and inequalities. Structuring an induction proof: base case, induction hypothesis, induction step, conclusion.

Vectors (ME-V1)

Two-dimensional vectors, vector arithmetic, magnitude and direction. The scalar (dot) product, the angle between two vectors, and orthogonality. Projection of one vector onto another. Parametric vector equations of lines. Geometric proofs using vectors.

Statistical analysis (ME-S1)

The Bernoulli trial, the binomial distribution, mean and variance of $X \sim B(n, p)$ , exact binomial probabilities, and the normal approximation of the binomial.

Exam structure

HSC Mathematics Extension 1 is sat as a single 2-hour paper plus 10 minutes reading time, in addition to the Mathematics Advanced paper.

Section I: Multiple choice, 10 questions, 10 marks
Section II: Free response, 14 questions, 60 marks

Total: 70 marks.

The paper covers both Year 11 and Year 12 Extension 1 content. Multi-step extended questions in the back third of Section II combine topics: a typical Q14 might thread vectors through a projectile problem, or combine induction with combinatorics.

Bring a NESA-approved scientific calculator. Graphics calculators are not used in NSW HSC Mathematics.

How Extension 1 scales (2026)

Mathematics Extension 1 typically scales to a mean scaled mark per unit of around 41-43 out of 50. It is consistently the second-highest-scaling HSC subject (behind Mathematics Extension 2) and lifts the overall ATAR aggregate significantly when sat alongside Advanced. For comparison:

Mathematics Extension 2: scales to around 46-47 per unit (highest most years)
Mathematics Extension 1: scales to around 41-43 per unit
Mathematics Advanced: scales to around 34-35 per unit
Mathematics Standard 2: scales to around 25 per unit

A raw HSC mark of 80 in Extension 1 (a Band E4) typically scales to about 47-48, which is exceptional for ATAR. Try our HSC ATAR calculator to model your projected ATAR from Extension 1 plus your other subjects.

Bands in Extension 1 are labelled E1 to E4 rather than 1 to 6 (because it is a 1-unit course). E4 starts at 80%, E3 at 65%, E2 at 50%. Most strong cohorts aim for E3 or E4.

Study strategy

Extension 1 rewards consistent weekly practice over short, intense cramming sessions. The standard approach is:

Master Advanced first. Extension 1 sits on top of Advanced calculus, functions and trig. If you cannot quickly differentiate a chain-rule composite or integrate by substitution, Extension 1 questions will be unforgiving.
Build the syllabus into a topic-by-topic checklist. Use the dot point pages on this site as your spine.
Drill standard techniques. Induction, integration by substitution, vector dot product, binomial probability and the t-formula are the bread and butter of the paper.
Do at least 8 full past papers under timed conditions in the final two terms. Mark them honestly against the NESA marking guidelines.
Keep a mistakes book. Note every careless slip and re-do the question a week later.

Our 2026 deep guides

We have written in-depth guides for the high-stakes Extension 1 topics:

Each guide includes worked examples, exam-style questions, and links to the relevant NESA syllabus dot points.

System context

HSC Mathematics Extension 1 sits inside the wider HSC system. Related explainers:

How the HSC ATAR is calculated covers UAC's aggregate and scaling mechanics.
How HSC subjects are scaled explains why Extension 1 scales much higher than Advanced or Standard.
HSC bonus points and EAS covers subject-specific selection-rank bonuses (Mathematics Extension 1 earns bonus points at most NSW engineering, science and actuarial degrees).

How to use this hub

If you are a Year 12 student sitting HSC 2026: work through every Year 12 module dot point on this site, then return to weak Year 11 dot points. Aim for 8 to 12 timed past papers in Term 4.

If you are a Year 11 student on the new 2024 syllabus: read the Year 11 dot points (Functions, Trig, Calculus, Combinatorics) carefully and start banking the Year 12 dot points as your school covers them.

For the official NESA syllabus, prescribed reference material, and past papers, refer to educationstandards.nsw.edu.au.

02-Guides

In-depth written guides with paired practice quizzes.

See all →

HSC Maths Extension 1 binomial theorem and combinatorics: deep dive (2026 guide)A complete deep dive into the binomial theorem and combinatorics for HSC Mathematics Extension 1. Counting principles, permutations, combinations, the binomial theorem in full, Pascal's triangle, standard exam techniques (general term, independent term, sum identities), and an embedded practice question set with full solutions.22 min read HSC Maths Extension 1 mathematical induction: deep dive (2026 guide)A complete deep dive into mathematical induction for HSC Mathematics Extension 1. The principle, the four-part structure, fully worked walkthroughs of all three flavours (series, divisibility, inequalities), the standard exam traps, and an embedded practice question set with full solutions.22 min read HSC Maths Extension 1 vectors: deep dive (2026 guide)A complete deep dive into vectors for HSC Mathematics Extension 1. Vector arithmetic, magnitude and unit vectors, the scalar product, projections, parametric vector equations of lines, geometric proofs, and an embedded practice question set with full solutions.22 min read

03-Practice quizzes

Binomial Theorem and Combinatorics (HSC Maths Extension 1, 2026)10 questions Mathematical Induction (HSC Maths Extension 1, 2026)10 questions Vectors (HSC Maths Extension 1, 2026)10 questions

04-The HSC system

general10 hardest HSC subjects in 2026 (and what 'hard' actually means)A ranked list of the 10 hardest HSC subjects in 2026 based on cohort strength, content difficulty, time commitment and band distribution. With the data, the honest reasons each subject earns its place, and why the answer to 'what is the hardest HSC subject' is more nuanced than a ranking.scaling10 highest scaling HSC subjects in 2026 (with UAC data)The 10 highest-scaling HSC subjects in 2026, ranked using the most recent publicly-released UAC scaling means. Plus what scaling actually does to your ATAR, when high scaling helps, and when it does not.generalAI and academic integrity in 2026: what you can and cannot doAn honest 2026 guide to how Year 12 students can use AI tools well and where the line is. NESA, VCAA, and QCAA rules, what AI is actually good at, what it is bad at, and how to think about it without panicking.wellbeingExam stress, anxiety, and looking after yourselfAn honest guide to exam stress and mental health in Year 12. What is normal, what is not, when to ask for help, and what to do if it gets really hard. With the numbers you can call.uni pathwaysGap year or uni straight after school?A clear-eyed comparison of going straight to uni versus taking a gap year. Who benefits from each, how to actually defer your offer, common gap-year traps, and how to make either path work for you.

05-Common questions

What is HSC Mathematics Extension 1?

Mathematics Extension 1 is a 1-unit NSW HSC course taken alongside Mathematics Advanced (the two together make a 3-unit study). It extends Advanced with proof by induction, further trigonometry, further calculus, vectors, the binomial distribution, polynomials, combinatorics and inverse trigonometric functions. The HSC paper is sat in addition to the Mathematics Advanced paper.

How is HSC Mathematics Extension 1 structured?

Extension 1 covers seven topic strands across Year 11 and Year 12. Year 11 modules are Functions (ME-F1, ME-F2), Trigonometric Functions (ME-T1, ME-T2), Calculus (ME-C1) and Combinatorics (ME-A1). Year 12 modules are Proof (ME-P1), Trigonometric Equations (ME-T3), Further Calculus Skills (ME-C2), Applications of Calculus (ME-C3), Vectors (ME-V1) and the Binomial Distribution (ME-S1). The HSC paper examines both Year 11 and Year 12 content.

How does HSC Mathematics Extension 1 scale?

Mathematics Extension 1 typically scales to a mean scaled mark per unit of around 41-43 out of 50. It is one of the highest-scaling HSC subjects most years, second only to Mathematics Extension 2. A raw HSC mark of 80+ (a Band E4) typically scales to a per-unit mark of around 47-48, which is extremely strong for ATAR.

What is the HSC Mathematics Extension 1 exam format?

The Mathematics Extension 1 HSC paper is 2 hours of working time plus 10 minutes reading time, worth 70 marks. Section I is 10 multiple choice questions for 10 marks. Section II is 14 free-response questions for 60 marks, ranging from short answers to longer multi-step problems. An approved scientific calculator is allowed; graphics calculators are not.

Is HSC Mathematics Extension 1 worth doing for ATAR?

For students aiming at 95+ ATAR with STEM, commerce or actuarial degrees, Extension 1 is one of the most efficient subjects to take. The scaling lift over Mathematics Advanced is substantial. The catch is that you must already be doing well in Advanced; a Band 4 in Advanced and a Band E1 in Extension 1 is worse than a Band 6 in Advanced alone, because the underperformance drags your aggregate down. Most strong cohorts treat Extension 1 as a baseline expectation.

How many past papers should I do for HSC Mathematics Extension 1?

Aim for 8-12 full past papers under timed conditions before the HSC, with detailed review of marking guidelines. The 2020-2024 Extension 1 papers are most relevant because they sit under the current 2017 syllabus. Older papers (pre-2018) used the previous 3 Unit Mathematics syllabus, which overlaps but has different emphasis and notation; use them for extra problem-solving practice rather than as exam dress rehearsals.